Useful Links
Physics
Classical Mechanics
Oscillatory Motion
Simple Harmonic Motion (SHM)
Characteristics and Definition
Periodicity and Sinusoidal Nature of SHM
Mathematical Representation: x(t) = A cos(ωt + φ)
Definitions and Units of Amplitude, Frequency, and Phase
Angular Frequency and its Relationship to Period
Spring-Mass Systems
Hooke's Law: F = -kx
Proportionality Constant (k) as Spring Constant
Analysis of Restoring Force as Function of Displacement
Energy in SHM
Kinetic Energy and Potential Energy in Springs
Conservation of Mechanical Energy
Deriving Motion Equations
Differential Equations: d²x/dt² + (k/m)x = 0
Real-world Applications
Measurements of Oscillations in Engineering
Vibrational Analysis in Mechanical Systems
Pendulums
Simple Pendulum
Derivation of Period: T = 2π√(l/g)
Assumptions: Small Angle Approximation
Analyzing Forces and Energies
Physical Pendulum
Extension to Compound Bodies
Calculating Periods for Irregular Shapes
Applications and Limitations
Use in Clocks and Timekeeping
Pendulum Designs in Engineering
Damped and Driven Harmonic Oscillators
Damped Oscillations
Types of Damping: Light, Critical, and Overdamping
Damping Equation: mx'' + bx' + kx = 0
Exponential Decay and Effect on Amplitude
Driven Oscillations
Forced Oscillators: Understanding Driving Forces
Resonance Phenomenon in Driven Systems
Steady-State Solution for Forced Oscillations
Phase Shift between Driving Force and Displacement
Resonance
Definition and Concepts
Natural Frequency and its Role in Resonance
Amplitude Response and Frequency Matching
Applications in Engineering and Science
Resonance in Bridges and Buildings
Tuning of Musical Instruments
Electromagnetic Resonance in Circuits
Risks and Mitigation Strategies
Structural Failure Due to Resonance
Designing for Damping and Control
5. Rigid Body Dynamics
First Page
7. Gravitation